There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person...

There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person committee. How many committees are possible containing at most 1 faculty member?

A. 112
B. 105
C. 277,200
D. 12,600
E. 12
F. 2310

Solutions

Expert Solution

Number of faculty member = 5

Number of students and office staff = 4+3 = 7

Number of committees possible to be formed with 1 faculty member = 7C5 5C1 = 21 5 = 105

Number of committees possible to be formed with no faculty member = 7C6 = 7

Number of committees possible to be formed containing at most 1 faculty member = (Number of committees possible to be formed with 1 faculty member + Number of committees possible to be formed with no faculty member)

Number of committees possible to be formed containing at most 1 faculty member = (105 + 7) = 112

Answer: A. 112

orchestra answered 1 year ago

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